Advertisements
Advertisements
Question
The nth term of an A.P. 5, 8, 11, 14, ...... is 68. Find n = ?
Solution
The given A.P. is 5, 8, 11, 14, ......
Here, a = 5, d = 8 – 5 = 3, tn = 68
Since tn = a + (n – 1)d,
68 = 5 + (n – 1)(3)
∴ 68 = 5 + 3n – 3
∴ 68 = 2 + 3n
∴ 66 = 3n
∴ n = `66/3`
∴ n = 22
APPEARS IN
RELATED QUESTIONS
If the 9th term of an A.P. is zero, then prove that 29th term is double of 19th term.
Decide whether the following sequence is an A.P., if so find the 20th term of the progression:
–12, –5, 2, 9, 16, 23, 30, ..............
Find the 19th term of the following A.P.:
7, 13, 19, 25, ...
Six year before, the age of mother was equal to the square of her son's age. Three year hence, her age will be thrice the age of her son then. Find the present ages of the mother and son.
Select the correct alternative and write it.
What is the sum of first n natural numbers ?
Select the correct alternative and write it.
If a share is at premium, then -
For a given A.P. a = 3.5, d = 0, then tn = _______.
If the sum of first n terms of an AP is n2, then find its 10th term.
How many multiples of 4 lie between 10 and 205?
Decide whether the given sequence 24, 17, 10, 3, ...... is an A.P.? If yes find its common term (tn)
How many two-digit numbers are divisible by 5?
Activity :- Two-digit numbers divisible by 5 are, 10, 15, 20, ......, 95.
Here, d = 5, therefore this sequence is an A.P.
Here, a = 10, d = 5, tn = 95, n = ?
tn = a + (n − 1) `square`
`square` = 10 + (n – 1) × 5
`square` = (n – 1) × 5
`square` = (n – 1)
Therefore n = `square`
There are `square` two-digit numbers divisible by 5
Decide whether 301 is term of given sequence 5, 11, 17, 23, .....
Activity :- Here, d = `square`, therefore this sequence is an A.P.
a = 5, d = `square`
Let nth term of this A.P. be 301
tn = a + (n – 1) `square`
301 = 5 + (n – 1) × `square`
301 = 6n – 1
n = `302/6` = `square`
But n is not positive integer.
Therefore, 301 is `square` the term of sequence 5, 11, 17, 23, ......
If tn = 2n – 5 is the nth term of an A.P., then find its first five terms
If p - 1, p + 3, 3p - 1 are in AP, then p is equal to ______.
Find a and b so that the numbers a, 7, b, 23 are in A.P.
In an A.P. if the sum of third and seventh term is zero. Find its 5th term.
Write the next two terms of the A.P.: `sqrt(27), sqrt(48), sqrt(75)`......
